It is given that the equations x2 minus y2 0 and x minus a 2 y2 1 have single po...........

Quantitative Aptitude (CDS) Quadratic Equations

It is given that the equations x² − y² = 0 and ( x − a )² + y² = 1 have single positive solution. For this, the value of ‘a’ is

$\sqrt{2}$

$-\sqrt{2}$

x² − y² = 0

x² = y²

( x − a )² + y² = 1

x² + a²- 2ax + y² = 1

x² + a²- 2ax + x² - 1 = 0

2x² - 2ax + a² - 1 = 0

For a single positive solution, D=0

b² - 4ac = 0

(-2a)² - 4(2)(a² - 1) = 0

Solving we get

a = $\pm \sqrt{2}$

As it has a single positive solution, that is only possible when a= $\pm \sqrt{2}$

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